Question

In the given figure, $△ABC$ and $△DEF$ are similar. BC = 3 cm, EF = 2 cm, and area of $△ABC=54c{m}^2$, then the area of $△DEF$ is __ $c{m}^2.$

• A. 28
• B. 22
• C. 24
• D. 26

Answer 1

The correct option is C 24

We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

$△ABC$ $\sim$ $△DEF$ (given)

$\Rightarrow \frac{Areaof△ABC}{Areaof△DEF}=\frac{B{C}^2}{E{F}^2}$

$\frac{54}{Areaof△DEF}=\frac{3^2}{2^2}$

$\frac{54}{Areaof△DEF}=\frac{9}{4}$

$Areaof△DEF=\frac{4\times 54}{9}=4\times 6=24c{m}^2$